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  • From: "K Randolph" <kwrandolph AT gmail.com>
  • To: "B Hebrew" <b-hebrew AT lists.ibiblio.org>
  • Subject: Re: [b-hebrew] Peter Kirk's homonym percentage table
  • Date: Sat, 20 Jan 2007 21:53:46 -0800

Peter:

I'm having an intuitive reaction that something doesn't seem right
here. I don't know enough to be able to tell what is wrong, but if the
formula is correct, it should not be giving the obviously incorrect
response for the resh.

I sent a copy of the spreadsheet with some explanatory info. to a
friend who has a PhD in statistics, but he hasn't responded yet.

Karl W. Randolph.

On 1/19/07, Peter Kirk <peter AT qaya.org> wrote:

The formula for H(1,A) etc is as given in my previous post: (1/2)N^2 *
p(1,A)^2 * sum of (p(2,B)^2) column * sum of (p(3,C)^2) column.

I noted also that for resh the estimated homonym probability is so high,
in fact nearly one in three, that the assumptions I was making break
down. My first estimate for the probable number of homonyms for each
root is (1/2)N^2 * (p(ABC))^2, or (to simplify) (Np)^2/2. But in fact
there are higher order terms here, to adjust for cases for three or more
homonyms, and I think the full formula comes to something like:

(Np)^2/2 - (Np)^3/6 + (Np)^4/24 - ...

Now if for a particular root the first estimate is 1/2, that implies
that (Np) = 1, and so the second term in the series is 1/6, the third is
1/24 etc etc., and the sum is just above 1/3. In fact for the root
nun-vav-resh (one of the most probable), p(ABC) =
(137/1615)*(175/1615)*(210/1615) = 0.001195, and (Np) = 1.93. With a
value of (Np) this high my approximations break down completely. As this
kind of breakdown is most common with resh and medial vav, and as the
expected effect is that the estimated number of homonyms should be
significantly reduced, it is not surprising that for vav and resh the
estimates proved to be significantly higher than expected.

What all of this shows me is that the observed distribution of homonyms
is very close to what would be expected from a random distribution of
verbs. That tells us something about how the roots are distributed. It
also, it seems to me, tells me that the people who detected homonyms
among these verbs are on the right track, for they are consistently
detecting the statistically expected number of homonyms.

PS Sorry if we are boring others on the list with this.

--
Peter Kirk
E-mail: peter AT qaya.org
Blog: http://speakertruth.blogspot.com/
Website: http://www.qaya.org/






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